Kaskade::DirichletPenaltyBoundary< GridView, components, ScalarType > Class Template Reference

Dirichlet boundary conditions by the penalty approach. More...

#include <boundaryConditions.hh>

Detailed Description

template<class GridView, int components, class ScalarType = typename GridView::ctype>
class Kaskade::DirichletPenaltyBoundary< GridView, components, ScalarType >

Dirichlet boundary conditions by the penalty approach.

For the Dirichlet boundary condition \( u|_{\partial \Omega} = u_D \), this defines the term \( \frac{\gamma}{2} h_F^{-2} |u-u_D|^2 \) (and its derivatives), which can be added to the variational functional. The scaling by the face diameter \( h_F \) is supposed to provide nearly optimal convergence rates for linear finite elements.

The dependence on \( h_F^{-2} \) can lead to ill-conditioned stiffness matrices on mesh refinement. Consider using DirichletNitscheBoundary instead.

Definition at line 88 of file boundaryConditions.hh.

Public Types
using	Vector = Dune::FieldVector< Scalar, components >

Public Member Functions
void	moveTo (typename GridView::IntersectionIterator const &fi)
	Moves the boundary condition to a new face. More...
void	setBoundaryData (Scalar gamma_, Vector const &u_, Vector const &ud)
	Defines the data for the boundary condition. More...
Scalar	d0 () const
Vector	d1 (VariationalArg< Scalar, dim > const &argT) const
Dune::FieldMatrix< Scalar, components, components >	d2 (VariationalArg< Scalar, dim > const &argTest, VariationalArg< Scalar, dim > const &argAnsatz) const

Member Typedef Documentation

Vector

template<class GridView , int components, class ScalarType = typename GridView::ctype>

using Kaskade::DirichletPenaltyBoundary< GridView, components, ScalarType >::Vector = Dune::FieldVector<Scalar,components>

Definition at line 96 of file boundaryConditions.hh.

Member Function Documentation

d0()

template<class GridView , int components, class ScalarType = typename GridView::ctype>

Scalar Kaskade::DirichletPenaltyBoundary< GridView, components, ScalarType >::d0 ( ) const

inline

Definition at line 129 of file boundaryConditions.hh.

d1()

template<class GridView , int components, class ScalarType = typename GridView::ctype>

Vector Kaskade::DirichletPenaltyBoundary< GridView, components, ScalarType >::d1 ( VariationalArg< Scalar, dim > const &  argT ) const

inline

Definition at line 131 of file boundaryConditions.hh.

d2()

template<class GridView , int components, class ScalarType = typename GridView::ctype>

Dune::FieldMatrix< Scalar, components, components > Kaskade::DirichletPenaltyBoundary< GridView, components, ScalarType >::d2 ( VariationalArg< Scalar, dim > const &  argTest, VariationalArg< Scalar, dim > const &  argAnsatz  ) const

inline

Definition at line 137 of file boundaryConditions.hh.

moveTo()

template<class GridView , int components, class ScalarType = typename GridView::ctype>

void Kaskade::DirichletPenaltyBoundary< GridView, components, ScalarType >::moveTo ( typename GridView::IntersectionIterator const &  fi )

inline

Moves the boundary condition to a new face.

This is called before calling d0,d1,d2 on a new face, and here the weight \( h_F^{-2} \) is computed once.

Definition at line 104 of file boundaryConditions.hh.

setBoundaryData()

template<class GridView , int components, class ScalarType = typename GridView::ctype>

void Kaskade::DirichletPenaltyBoundary< GridView, components, ScalarType >::setBoundaryData ( Scalar  gamma_, Vector const &  u_, Vector const &  ud  )

inline

Defines the data for the boundary condition.

Call this from the evaluateAt method in the derived class.

Parameters

gamma	the nominal penalty factor (which is internally multiplied by h^{-2} to ensure convergence).
u	the displacement around which is linearized
ud	the given Dirichlet boundary value

Definition at line 121 of file boundaryConditions.hh.

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The documentation for this class was generated from the following file:

• boundaryConditions.hh